Question: Vanessa is 8 years younger than Tiffany. Tiffany and Vanessa first met 3 years ago. Sixteen years ago, Tiffany was 3 times older than Vanessa. How old is Tiffany now?
Solution: We can use the given information to write down two equations that describe the ages of Tiffany and Vanessa. Let Tiffany's current age be $t$ and Vanessa's current age be $v$ The information in the first sentence can be expressed in the following equation: $t = v + 8$ Sixteen years ago, Tiffany was $t - 16$ years old, and Vanessa was $v - 16$ years old. The information in the second sentence can be expressed in the following equation: $t - 16 = 3(v - 16)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $t$ , it might be easiest to solve our first equation for $v$ and substitute it into our second equation. Solving our first equation for $v$ , we get: $v = t - 8$ . Substituting this into our second equation, we get the equation: $t - 16 = 3($ $(t - 8)$ $ -$ $ 16)$ which combines the information about $t$ from both of our original equations. Simplifying the right side of this equation, we get: $t - 16 = 3t - 72$ Solving for $t$ , we get: $2 t = 56$ $t = 28$.